Preferential Semantics using Non-smooth Preference Relations

Frederik Van De Putte*, Christian Strasser

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)


This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation a parts per thousand(0) . They are equivalent to Shoham's so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After discussing this type of semantics, we focus on some concrete proposals from the literature, checking a number of meta-theoretic properties and elaborating on their intuitive motivation. As it turns out, many of their meta-properties only hold in case a parts per thousand(0) is transitive. To tackle this problem, we propose slight modifications of each of the systems, showing the resulting logics to behave better at the intuitive level and in metatheoretic terms, for arbitrary a parts per thousand(0) .
Original languageEnglish
Pages (from-to)903-942
Number of pages40
JournalJournal of Philosophical Logic
Issue number5
Publication statusPublished - Oct 2014
Externally publishedYes


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